Despite intensive investigations over the past five decades, the microscopic origins of the fascinating dielectric properties of $AB{\mathrm{O}}_3$ relaxor ferroelectrics are currently poorly understood. Here, we show that the frequency dispersion that is the hallmark of relaxor behavior is quantitatively related to the crystal chemical characteristics of the solid solution. Density functional theory is used in conjunction with experimental determination of cation arrangement to identify the 0 K structural motifs. These are then used to parametrize a simple phenomenological Landau theory that predicts the universal dependence of frequency dispersion on the solid solution cation arrangement and off-center cation displacements.

• Received 11 July 2006

DOI:https://doi.org/10.1103/PhysRevLett.99.267603